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Introduction to

Fading Channels, part 1

Dr. Essam SourourAlexandria University, Faculty of Engineering, Dept. Of Electrical

Engineering

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• Characterization of Fading Channels

• Large Scale Fading

• Short Scale Fading

• Fading Counter Measures

Section Overview

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• Two main effects:– Large Scale– Small Scale

• Large Scale Fading– Depends on environment and topology– Path Loss, Shadowing

• Small Scale Fading– Faster Changes– Depends on signal parameters

Characterization

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Small Scale and Large Scale Fading

Distance

ReceivedPower

dBDistance

effect

Shadowingeffect

Small ScaleFading

Characterization, cont.

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• For Open Areas use Line of Sight (LOS):

• Path Loss L (in dB) in far field:

Loss(dB) 20 log d• Loss with distance follows 20 dB/Octave

0

220

2 24t r

r t d

G G dP d P P

dd

Line of Sight (LOS)

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Loss(dB) 40 log d• Loss with distance follows 40 dB/Octave• In General, with many rays

Loss(dB) 10 log d• The loss exponent depends on environment

Cell phone

2 2

4t r t r

r t

G G h hP d P

d

2~3Obstructed in factories3 ~ 5Shadowed Urban

4~6Obstructed in building2.7~3.5Urban

1.6~1.8In-building LOS2Free Space

EnvironmentEnvironment

Path Loss with Distance

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• Most famous model: Okumura-Hata

• Okumura made extensive measurements• Hata transformed Okumura’s plots to an

empirical model• Valid for 150-1500 MHz • Model takes the effect of

– Transmitter height hb in m

– receiver height hm in m

– frequency fc in MHz

– Distance d in km– different environments

Hata Propagation Model

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log

( ) log

log

A B d Urban

L dB A B d C Suburban

A B d D open

2

2

69.55 26.16log 13.82log

44.9 6.55log

5.4 2 log 28

40.94 4.78 log 19.33 log

c b m

b

c

c c

A f h a h

B h

C f

D f f

2

2

1.1 log 0.7 1.56 log 0.8

8.28 log 1.54 1.1 400 ,

3.2 log 11.75 4.97 400 ,

c m c

m m c

m c

f h f Medium or small city

a h h f Mhz large city

h f Mhz large city

Hata’s Model

COST 231 Extension to Hata

• The European Cooperative for Scientific and Technical Research (COST) extended Hata model to 2GHz

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46.3 33.9 log 13.82log

44.9 6.55log log

c b m

b

L dB f h a h

h d C

0 mediumcityor suburb

3 metropolitan area

dBC

dB

• Valid for 1.5 Ghz<fc<2 GHz, 30 m<hb<200 m

and 1 m<hm<10 m

Indoor Propagation Loss (ITU-R P1238-1

• Simple ITU model for WPAN:

L(dB) = 20 log(f ) + N log(d) + Lf (n) − 28

• N =Distance Power Loss Coefficient

• f =Frequency (MHz)

• d =Distance (m) between nodes (d > 1)

• Lf =Floor Penetration Loss Factor (dB)

• n =Number of Floors Penetrated (n > 0)

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Indoor Model Parameters

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• In addition, indoor obstacles add more losses

• Extensive measurements made. Tables available in literature

• For example:– Concrete wall, 8 to 15 dB– Concrete floor, 10 dB– Foil insulation, 3.9 dB

Indoor Effects

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• Surrounding Environment varies, even at same distance from Tx

• Path Loss is random, with an average that depends on distance and frequency

• Distribution, in dB, found to be Gaussian

• Denoted by Log-Normal Shadowing

• Over and above loss due to distance

Shadowing Loss

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• L(dB)|d = L(dB)|do + 10 log (d/do) + X

• X is Gaussian with zero mean and standard deviation

• depends on environment, increases with more variations

• Outdoor: = 5 ~ 12 dB, typical 8 dB

• Hence, L(dB) is Gaussian with mean given by any of the distance-based relations, and standard deviation

Shadowing Loss, Cont.

Indoor Shadowing

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Indoor shadowing standard deviation for ITU-R P.1238-1 model

Total Effect

• In all previous models the received power at distance

• Where

• The value of , K and Kdo depends on frequency and environment

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10 log

10 logo

rec t

t

t d o

P dB P dB L dB

P dB K dB d X

P dB K dB d d X

10 logod oK dB K dB d

Cell Coverage Area

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• Coverage may be defined as the percentage of the area of the cell that receive power > Pmin

• C=covered area inside cell / cell area

• C 1

Coverage calculation, 1

• Received power Prec(x) at any distance r is Gaussian, with:– Mean dB (r) which depends on r, given by any of the

previous relations (LOS, two paths, Hata, or COST-231)– Standard deviation that depends on location

• Define F(r) as the probability Prec(x) exceeds Pmin

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min

min min1

2 2

rec

P

dB dB

F r P x dx

P r P rerfc Q

10 logodB t d or P dB K dB r d

Coverage calculation, 2

• On the average, the part of the area dA with received power > Pmin is : F (r) dA

• The total area (yellow part) in the cell with received power > Pmin is :

• Hence, the coverage C is given by:

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A

F r dA

2

2 20 0 0

1

1 2

A

R R

C F r dAA

F r r d dr r F r drR R

Coverage calculation, 3

• F(r) can be written as:

• Using integral (2.58) in textbook, we get

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lnr

F r Q a bR

min 10 log

10 log

ot d oP P K R da

eb

2

2 2 2exp

ab abC Q a Q

b b

Coverage calculation, 4

• Note that, without shadowing, the received power at cell border is given by:

• If we transmit enough power Pt such that Prec(at R)=Pmin , then a=0 and Q(a)=0.5

• In this case:

• Also, if there is no shadowing, =0, b= and C=1

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10 logorec t d oP at R P K R d

2

1 2 2exp

2C Q

b b

Homework

• Please solve the following problems from Chapter 2 of the textbook:

• Problems: 1, 13, 14, 15, 17, 19, 21, 23, 24, 25

• You may use any of the models in the lecture but specify in your answer which propagation model you are using.

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